We can’t know for sure if Gertrude was sleeping with Claudius while still married to Hamlet’s father, though Hamlet and the Ghost imply that she was. Both Hamlet and the Ghost call Claudius “adulterate,” which means “corrupted by adultery.” The Ghost also calls Gertrude “seeming-virtuous” (I.iv.), which suggests he believes he was wrong to trust her when he was alive. However, when Claudius confesses to the murder of his brother, he counts Gertrude among the “effects for which I did the murder” (III.iii.), suggesting he did not “possess” her before his brother’s death—although in this context “possess” might refer to marriage rather than to sexual intimacy. Furthermore, when Hamlet accuses Gertrude of “an act / That blurs the grace and blush of modesty” (III.iv.), Gertrude at first seems to have no idea what he’s talking about: “what act / That roars so loud[?]” (III.iv.). Later, however, she confesses that Hamlet’s words have made her see “black and grieved spots” (III.iv.) on her soul, which indicates that she feels guilty about something, although she doesn’t specify the source of her guilt. Once again, Shakespeare leaves the matter of sex ambiguous.